Permutations, cycles, and the pattern 2-13

2006/07/31 by Robert Parviainen, Parviainen, Robert
Mathematics · #05C05 #05C15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C05 #msc:05C15

paper · pdf · doi:10.48550/arxiv.math/0607793

13 pages, 1 figure

arxiv created 2006/07/31 · arxiv updated 2009/12/01

Abstract

We count the number of occurrences of restricted patterns of length 3 in permutations with respect to length and the number of cycles. The main tool is a bijection between permutations in standard cycle form and weighted Motzkin paths.

Related

• Pattern-restricted permutations composed of 3-cycles
• Pattern Count on Multiply Restricted Permutations
• Pattern-restricted permutations of small order
• Cycles and patterns in permutations
• Enumeration of permutations containing a prescribed number of occurrences of a pattern of length 3